{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# 1. Introduction\n",
    "\n",
    "### *Table of Contents*\n",
    "\n",
    "* 1.1 [Example: Polynomial Curve Fitting](#1.1-Example:-Polynomial-Curve-Fitting)\n",
    "* 1.2 [Probability Theory](#1.2-Probability-Theory)\n",
    "    * 1.2.1 [Probability densities](#1.2.1-Probability-densities)\n",
    "    * 1.2.2 [Expectations and covariances](#1.2.2-Expectations-and-covariances)\n",
    "    * 1.2.4 [The Gaussian distribution](#1.2.4-The-Gaussian-distribution)\n",
    "    * 1.2.5 [Curve fitting re-visited](#1.2.5-Curve-fitting-re-visited)\n",
    "* 1.6 [Information Theory](#1.6-Information-Theory)\n",
    "    * 1.6.1 [Relative entropy and mutual information](#1.6.1-Relative-entropy-and-mutual-information)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from prml.datasets import generate_toy_data\n",
    "from prml.preprocessing import PolynomialFeature\n",
    "from prml.linear.linear_regression import LinearRegression\n",
    "from prml.linear.ridge_regression import RidgeRegression\n",
    "from prml.distribution import Gaussian, MultivariateGaussian\n",
    "\n",
    "# Set random seed to make deterministic\n",
    "np.random.seed(0)\n",
    "\n",
    "# Ignore zero divisions and computation involving NaN values.\n",
    "np.seterr(divide=\"ignore\", invalid=\"ignore\")\n",
    "\n",
    "# Enable higher resolution plots\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## 1.1. Example: [Polynomial Curve Fitting](https://machinelearningcompass.com/machine_learning_models/linear_regression)\n",
    "\n",
    "For presentation purposes, consider a synthetically generated example dataset. The data were generated from the function $\\sin(2\\pi x)$ by adding random Gaussian noise having standard deviation $\\sigma=0.3$.\n",
    "\n",
    "We generated $N=10$ observations spaced uniformly in range $[0,1]$. These observations comprise the input data vector,\n",
    "\n",
    "$$\n",
    "\\mathsf{x} = (x_1,\\dots,x_N)^\\text{T}\n",
    "$$\n",
    "\n",
    "For each generated observation $x$ we obtained its corresponding value of the function $\\sin(2\\pi x)$ and then adding the random noise to capture the real-life situation of missing information.\n",
    "\n",
    "$$\n",
    "\\mathsf{t} = (t_1,\\dots,t_N)^\\text{T}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 266,
       "width": 398
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Sine function\n",
    "def sin(x: np.ndarray) -> np.ndarray:\n",
    "    return np.sin(2 * np.pi * x)\n",
    "\n",
    "\n",
    "# Generate a train data set\n",
    "x_train, y_train = generate_toy_data(sin, 10, 0.3)\n",
    "\n",
    "# Generate a test data set\n",
    "x_test = np.linspace(0, 1, 100)\n",
    "y_test = sin(x_test)\n",
    "\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", s=50, label=\"Training data\")\n",
    "plt.plot(x_test, y_test, color=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "plt.xlabel(\"$x$\", fontsize=14)\n",
    "plt.ylabel(\"$y$\", fontsize=14)\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The generated training dataset of $N=10$ points is shown as blue circles, each comprising an observation of the input variable $x$ along with the corresponding target variable $t$. The green curve shows the function $\\sin(2\\pi x)$ used to generate the data.\n",
    "\n",
    "### Polynomial Linear Model\n",
    "\n",
    "Our goal is to predict the value of $\\hat{t}$ for some **new** value of $\\hat{x}$, in the absence of any knowledge for the green curve. To that end, we consider a simple approach based on curve fitting. In particular, we shall try to fit the data using a polynomial function of the form\n",
    "\n",
    "$$\n",
    "y(x, \\mathbf{w}) = w_0 + w_1x + w_2x^2 + \\dots + w_Mx^M = \\sum_{j=0}^M w_jx^j\n",
    "$$\n",
    "\n",
    "where $M$ is the *order* of the polynomial. Functions, such as $y(x, \\mathbf{w})$, that are linear functions of the unknown coefficients $\\mathbf{w}$, are called *linear models*.\n",
    "\n",
    "### Error Function\n",
    "\n",
    "Next, we need to determine the values of the coefficients $\\mathbf{w}$ by fitting the polynomial to the training data. This can be done by minimizing an *error function* that measures the misfit between the function $y(x,\\mathbf{w})$, for a given value of $\\mathbf{w}$, and the training data points.\n",
    "\n",
    "One simple error function is the *sum of squares of the errors* between $y(x,\\mathbf{w})$ and the corresponding target values $t_n$\n",
    "\n",
    "$$\n",
    "E(\\mathbf{w}) = \\frac{1}{2}\\sum_{n=1}^N (y(x,\\mathbf{w}) - t_n)^2 \\geq 0\n",
    "$$\n",
    "\n",
    "where the function becomes zero if, and only if, the function $y(x,\\mathbf{w})$ were to pass\n",
    "exactly through each training data point.\n",
    "\n",
    "We can solve the curve fitting problem by choosing the value of $\\mathbf{w}$ for which $E(\\mathbf{w})$ is as small as possible. Because the error function is quadratic, its derivatives are linear, and so the minimization of the function has a unique closed from solution, denoted by $\\mathbf{w}^\\star$. To minimize the error function we should derive the gradient vector, set it equal to zero and solve for $\\mathbf{w}^\\star$ as follows,\n",
    "\n",
    "$$\n",
    "\\nabla E(\\mathbf{w}^\\star) = \\mathbf{0}\n",
    "$$\n",
    "\n",
    "First, we have to substitute the polynomial into the error function\n",
    "\n",
    "$$\n",
    "E(\\mathbf{w}) = \\frac{1}{2}\\sum_{n=1}^N \\Big(\\sum_{j=0}^M w_jx_n^j - t_n \\Big)^2\n",
    "$$\n",
    "\n",
    "Note that each of the $N$ data points from the generated training set has $1$ dimension, that is $x \\in \\mathbb{R}$. However, the polynomial function populates $M$ features for each input $x$, essentially transforming $x$ into a $M$-dimensional vector. Thus, the training set $\\mathsf{x}$ can be written as a $N\\times M$ matrix $\\mathbf{X}$ where $\\mathbf{X}_{nj}$ represents $x_n^j$, that is, the $n$th input value raised in the power of $j$.\n",
    "\n",
    "To find the gradient vector, we take the partial derivative of $E$ with respect to an arbitrary $w_k$. Differentiating the sum, term by term, we get\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\nabla E(\\mathbf{w}^\\star)_k &= \\frac{\\partial}{\\partial w_k} (\\mathbf{w}) \\\\\n",
    "&= \\frac{1}{2}\\sum_{n=1}^N 2 (\\sum_{j=0}^M w_jx_n^j - t_n)x_n^k\n",
    "= \\sum_{n=1}^N (\\sum_{j=0}^M w_jx_n^j - t_n)x_n^k \\\\\n",
    "&= \\sum_{n=1}^N (\\mathbf{X}\\mathbf{w} - \\mathsf{t})_n\\mathbf{X}_{nk}\n",
    "= \\sum_{n=1}^N \\mathbf{X}_{kn}^\\text{T}(\\mathbf{X}\\mathbf{w} - \\mathsf{t})_n \\\\\n",
    "&= \\big(\\mathbf{X}^\\text{T}(\\mathbf{X}\\mathbf{w} - \\mathsf{t})\\big)_k\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Using the partial derivative for one component, we compute the gradient vector by dropping the $k$ subscript. Thus, the minimizer $\\mathbf{w}^\\star$ must satisfy\n",
    "\n",
    "$$\n",
    "\\nabla E(\\mathbf{w}^\\star) = \\mathbf{X}^\\text{T}(\\mathbf{X}\\mathbf{w}^\\star - \\mathsf{t}) = \\mathbf{0}\n",
    "$$\n",
    "\n",
    "Solving for $\\mathbf{w}^\\star$ gives the unique solution of the curve fitting problem\n",
    "\n",
    "$$\n",
    "\\mathbf{X}^\\text{T}(\\mathbf{X}\\mathbf{w}^\\star - \\mathsf{t}) = \\mathbf{0} \\Leftrightarrow\n",
    "\\mathbf{X}^\\text{T}\\mathbf{X}\\mathbf{w}^\\star = \\mathbf{X}^\\text{T}\\mathsf{t} \\Leftrightarrow\n",
    "\\mathbf{w}^\\star = (\\mathbf{X}^\\text{T}\\mathbf{X})^{-1}\\mathbf{X}^\\text{T}\\mathsf{t}\n",
    "$$\n",
    "\n",
    "The resulting polynomial is given by the function $y(x, \\mathbf{w}^\\star)$.\n",
    "\n",
    "### Model Selection\n",
    "\n",
    "There remains the problem of choosing the order $M$ of the polynomial, which is an example of the important concept called *model selection*.\n",
    "\n",
    "In order to study the effect of different $M$ values, we plot the result of fitting polynomials having orders $M=0,1,3,9$ to the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 280,
       "width": 571
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i, degree in enumerate([0, 1, 3, 9]):\n",
    "    plt.subplot(2, 2, i + 1)\n",
    "    plt.tight_layout()\n",
    "\n",
    "    feature = PolynomialFeature(degree)\n",
    "    x_train_features = feature.transform(x_train)\n",
    "    x_test_features = feature.transform(x_test)\n",
    "\n",
    "    model = LinearRegression()\n",
    "    model.fit(x_train_features, y_train)\n",
    "    y, _ = model.predict(x_test_features)\n",
    "\n",
    "    plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", s=50, label=\"Training data\")\n",
    "    plt.plot(x_test, y_test, color=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "    plt.plot(x_test, y, color=\"r\", label=\"Fitting\")\n",
    "    plt.ylim(-2, 2)\n",
    "    plt.title(\"$M={}$\".format(degree), fontsize=14)\n",
    "\n",
    "plt.legend(bbox_to_anchor=(1, 0.85), loc=2, borderaxespad=1, fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Note that the constant ($M=0$) and first order ($M=1$) polynomials give rather poor fits to the data. The third order ($M=3$) polynomial seems to give the best fit, while the higher order one ($M=9$) achieves an excellent fit to the data, that is, $E(\\mathbf{w}^\\star) = \\mathbf{0}$. However, the fitted curve gives a poor representation of the underlying function $\\sin(2\\pi x)$. This phenomenon is known as *over-fitting*.\n",
    "\n",
    "A more quantitative insight into the generalization performance on $M$ can be obtained by using the *root-mean-square* (RMS) error defined as\n",
    "\n",
    "$$\n",
    "E_{RMS} = \\sqrt{2\\frac{E(\\mathbf{w}^\\star)}{N}}\n",
    "$$\n",
    "\n",
    "The RMS error on both training and test data points for each value of $M$ is shown in the following figure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 268,
       "width": 391
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def rms_error(a, b):\n",
    "    return np.sqrt(2 * np.mean(np.square(a - b)))\n",
    "\n",
    "\n",
    "training_errors = []\n",
    "test_errors = []\n",
    "\n",
    "for i in range(10):\n",
    "    feature = PolynomialFeature(i)\n",
    "    x_train_features = feature.transform(x_train)\n",
    "    x_test_features = feature.transform(x_test)\n",
    "\n",
    "    model = LinearRegression()\n",
    "    model.fit(x_train_features, y_train)\n",
    "    y, _ = model.predict(x_test_features)\n",
    "    training_errors.append(rms_error(model.predict(x_train_features), y_train))\n",
    "    test_errors.append(\n",
    "        rms_error(model.predict(x_test_features), y_test + np.random.normal(scale=0.3, size=len(y_test)))\n",
    "    )\n",
    "\n",
    "plt.plot(training_errors, \"o-\", mfc=\"none\", mec=\"b\", ms=10, c=\"b\", label=\"Training error\")\n",
    "plt.plot(test_errors, \"o-\", mfc=\"none\", mec=\"r\", ms=10, c=\"r\", label=\"Test error\")\n",
    "plt.xlabel(\"$M$\", fontsize=14)\n",
    "plt.ylabel(\"$E_{RMS}$\", fontsize=14)\n",
    "plt.legend(fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test set error is measuring how well we are doing in predicting the values of $t$ for new data observations of $x$. For $M=9$, the training set error goes to zero, because the polynomial contains $10$ degrees of freedom and so it can be tuned exactly to the $10$ data points in the training set.\n",
    "\n",
    "It is also interesting to examine the behavior of the model as the size of the data increases. The following figure depicts the result of fitting the $M=9$ polynomial for $N=15$ and $N=100$ data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 265,
       "width": 535
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i, size in enumerate([15, 100]):\n",
    "    plt.subplot(1, 2, i + 1)\n",
    "\n",
    "    # Generate a train set\n",
    "    x_train_100, y_train_100 = generate_toy_data(sin, size, 0.3)\n",
    "\n",
    "    # Generate a test set\n",
    "    x_test_100 = np.linspace(0, 1, 100)\n",
    "    y_test_100 = sin(x_test)\n",
    "\n",
    "    feature = PolynomialFeature(9)\n",
    "    x_train_100_features = feature.transform(x_train_100)\n",
    "    x_test_100_features = feature.transform(x_test_100)\n",
    "\n",
    "    model = LinearRegression()\n",
    "    model.fit(x_train_100_features, y_train_100)\n",
    "    y, _ = model.predict(x_test_100_features)\n",
    "\n",
    "    plt.scatter(x_train_100, y_train_100, facecolor=\"none\", edgecolor=\"b\", s=50, label=\"Training data\")\n",
    "    plt.plot(x_test_100, y_test_100, color=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "    plt.plot(x_test_100, y, color=\"r\", label=\"Fitting\")\n",
    "    plt.ylim(-1.5, 1.5)\n",
    "    plt.title(\"$N={}$\".format(size), fontsize=14)\n",
    "\n",
    "plt.legend(bbox_to_anchor=(1, 0.64), loc=2, borderaxespad=1, fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Note that the over-fitting problem becomes less severe as the size of the data set increases. In other words, the larger the data set, the more complex the model that we can afford to fit to the data.\n",
    "\n",
    "### Regularization\n",
    "\n",
    "One technique that is often used to control the over-fitting phenomenon is that of *regularization*, which adds a penalty term to the error function in order to discourage the coefficients from reaching large values. The simplest such penalty term is the sum of squares of all of the coefficients, leading to a modified error function of the following form\n",
    "\n",
    "$$\n",
    "\\tilde{E}(\\mathbf{w}) = \\frac{1}{2}\\sum_{n=1}^N (y(x,\\mathbf{w}) - t_n)^2 + \\lambda||\\mathbf{w}||_2^2\n",
    "$$\n",
    "\n",
    "Such techniques are known as *shrinkage* methods because they reduce the value of the coefficients. The particular case of the quadratic regularization is called *ridge regression*. In neural networks, this approach is also known as *weight decay*.\n",
    "\n",
    "Similar to the previous case, the ridge error function can be minimized exactly in closed form as follows,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\nabla E(\\mathbf{w}^\\star)_k &= \\frac{\\partial}{\\partial w_k} (\\mathbf{w}) \\\\\n",
    "&= \\frac{1}{2}\\sum_{n=1}^N 2 (\\sum_{j=0}^M w_jx_n^j - t_n)x_n^k + \\frac{1}{2}\\lambda 2w_k \\\\\n",
    "&= \\sum_{n=1}^N (\\sum_{j=0}^M w_jx_n^j - t_n)x_n^k + \\lambda w_k \\\\\n",
    "&= \\sum_{n=1}^N (\\mathbf{X}\\mathbf{w} - \\mathsf{t})_n\\mathbf{X}_{nk} + \\lambda w_k\n",
    "= \\sum_{n=1}^N \\mathbf{X}_{kn}^\\text{T}(\\mathbf{X}\\mathbf{w} - \\mathsf{t})_n + \\lambda w_k \\\\\n",
    "&= \\big(\\mathbf{X}^\\text{T}(\\mathbf{X}\\mathbf{w} - \\mathsf{t})\\big)_k + \\lambda w_k\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Using the partial derivative for one component, we compute the gradient vector by dropping the $k$ subscript. Then, the minimizer $\\mathbf{w}^\\star$ must satisfy\n",
    "\n",
    "$$\n",
    "\\nabla E(\\mathbf{w}^\\star) =\n",
    "\\mathbf{X}^T(\\mathbf{X}\\mathbf{w}^\\star - \\mathsf{t}) + \\lambda\\mathbf{w}^\\star\\mathbf{I}= \\mathbf{0}\n",
    "$$\n",
    "\n",
    "Solving for $\\mathbf{w}^\\star$ gives the unique solution that minimizes the ridge error\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& \\mathbf{X}^\\text{T}(\\mathbf{X}\\mathbf{w}^\\star - \\mathsf{t}) + \\lambda\\mathbf{w}^\\star\\mathbf{I} = \\mathbf{0} \\Leftrightarrow \\\\\n",
    "& \\mathbf{X}^\\text{T}\\mathbf{X}\\mathbf{w}^\\star - \\mathbf{X}^\\text{T}\\mathsf{t} + \\lambda\\mathbf{w}^\\star\\mathbf{I} = \\mathbf{0} \\Leftrightarrow \\\\\n",
    "& \\mathbf{X}^\\text{T}\\mathbf{X}\\mathbf{w}^\\star + \\lambda\\mathbf{w}^*\\mathbf{I} = \\mathbf{X}^\\text{T}\\mathsf{t} \\Leftrightarrow \\\\\n",
    "& \\mathbf{w}^\\star(\\mathbf{X}^\\text{T}\\mathbf{X} + \\lambda\\mathbf{I}) = \\mathbf{X}^\\text{T}\\mathsf{t} \\Leftrightarrow \\\\\n",
    "& \\mathbf{w}^\\star = (\\mathbf{X}^\\text{T}\\mathbf{X} + \\lambda\\mathbf{I})^{-1}\\mathbf{X}^\\text{T}\\mathsf{t}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "The following figures depict the results of fitting the polynomial of order $M=9$ to the same data set as before but this time using the regularized error function. We see that, for a value of $\\ln\\lambda=−18$, the over-fitting has been suppressed and we obtain a much closer representation of the underlying function $\\sin(2\\pi x)$. If, however, we use too large a value for $\\lambda$ then we again obtain a poor fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 279,
       "width": 571
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "feature = PolynomialFeature(9)\n",
    "x_train_features = feature.transform(x_train)\n",
    "x_test_features = feature.transform(x_test)\n",
    "\n",
    "for i, ln_lambda in enumerate([float(\"-inf\"), -18, 0]):\n",
    "    plt.subplot(1, 3, i + 1)\n",
    "    plt.tight_layout()\n",
    "\n",
    "    model = RidgeRegression(alpha=math.exp(ln_lambda))\n",
    "    model.fit(x_train_features, y_train)\n",
    "    y, _ = model.predict(x_test_features)\n",
    "\n",
    "    plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", s=50, label=\"Training data\")\n",
    "    plt.plot(x_test, y_test, color=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "    plt.plot(x_test, y, color=\"r\", label=\"Fitting\")\n",
    "    plt.ylim(-2, 2)\n",
    "    plt.title(\"$\\ln\\lambda={}$\".format(ln_lambda), fontsize=14)\n",
    "\n",
    "plt.legend(bbox_to_anchor=(1, 0.65), loc=2, borderaxespad=1, fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "A sample of coefficients from the fitted polynomials is presented in the table below, showing that regularization has the desired effect of reducing the magnitude of the coefficients.\n",
    "\n",
    "| $\\ln\\lambda{=}-\\infty$ | $\\ln\\lambda{=}-18$ | $\\ln\\lambda{=}0$ |\n",
    "|-----------------------:|-------------------:|-----------------:|\n",
    "|                 $0.39$ |             $0.38$ |           $0.36$ |\n",
    "|              $-135.04$ |            $-2.14$ |          $-0.46$ |\n",
    "|              $3206.76$ |            $81,88$ |          $-0.39$ |\n",
    "|            $-29215.92$ |          $-390.51$ |          $-0.22$ |\n",
    "|            $139594.34$ |           $578.12$ |          $-0.05$ |\n",
    "|           $-388863.80$ |           $-31.48$ |           $0.07$ |\n",
    "|            $652373.24$ |           $-49.12$ |           $0.17$ |\n",
    "|           $-648124.69$ |           $-28.57$ |           $0.25$ |\n",
    "|            $350721.94$ |           $540.17$ |           $0.31$ |\n",
    "|            $-79556.29$ |          $-255.65$ |           $0.35$ |\n",
    "\n",
    "The impact of the regularization term on the generalization error can be seen by plotting the value of the RMS error for both training and test sets against $\\ln\\lambda$, as shown in the next figure. We see that $\\lambda$ controls the effective complexity of the model and hence determines the degree of over-fitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 266,
       "width": 391
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "training_errors = []\n",
    "test_errors = []\n",
    "\n",
    "feature = PolynomialFeature(9)\n",
    "x_train_features = feature.transform(x_train)\n",
    "x_test_features = feature.transform(x_test)\n",
    "\n",
    "ln_lambda_values = range(-40, -20, 1)\n",
    "for ln_lambda in ln_lambda_values:\n",
    "    model = RidgeRegression(alpha=math.exp(ln_lambda))\n",
    "    model.fit(x_train_features, y_train)\n",
    "    training_errors.append(rms_error(model.predict(x_train_features)[0], y_train))\n",
    "    test_errors.append(\n",
    "        rms_error(model.predict(x_test_features)[0], y_test + np.random.normal(scale=0.3, size=len(y_test)))\n",
    "    )\n",
    "\n",
    "plt.plot(ln_lambda_values, training_errors, mfc=\"none\", mec=\"b\", ms=10, c=\"b\", label=\"Training error\")\n",
    "plt.plot(ln_lambda_values, test_errors, mfc=\"none\", mec=\"r\", ms=10, c=\"r\", label=\"Test error\")\n",
    "plt.xlabel(\"$\\ln\\lambda$\", fontsize=14)\n",
    "plt.ylabel(\"$E_{RMS}$\", fontsize=14)\n",
    "plt.legend(fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# 1.2 [Probability Theory](https://seeing-theory.brown.edu)\n",
    "\n",
    "The probability $p(A)$ of an event $A$ is always a non-negative number, i.e.,\n",
    "\n",
    "$$\n",
    "p(A) \\geq 0\n",
    "$$\n",
    "\n",
    "The probability $p(B)$ of an event $B$ which is certain to occur is always equal to one, i.e.,\n",
    "\n",
    "$$\n",
    "p(B) = 1\n",
    "$$\n",
    "\n",
    "In case two events $A$ and $B$ are **mutually exclusive**, that is, they cannot occur simultaneously $p(A \\cap B)=0$, then the probability of occurrence of either $A$ or $B$ is denoted as $A \\cup B$ and is given by\n",
    "\n",
    "$$\n",
    "p(A \\cup B) = p(A) + p(B) - 2p(A \\cap B) = p(A) + p(B)\n",
    "$$\n",
    "\n",
    "![Venn](../images/venn.png)\n",
    "\n",
    "### Rules of Probability\n",
    "\n",
    "Consider the slightly more general example involving two random variables $X$ and $Y$ instead of just two events (which are essentially binary random variables). Suppose that $X$ can take any of the values $x_i$, and $Y$ can take the values $y_j$. Moreover, consider a total of $N$ trials, and let the number of such trials in which $X=x_i$ and $Y=y_j$ be $n_{ij}$. Also, let the number of trials in which $X$ takes the value $x_i$ (irrespective of the value that $Y$ takes) be denoted by $c_i$, and similarly let the number of trials in which $Y$ takes the value $y_j$ be denoted by $r_j$.\n",
    "\n",
    "<img src=\"../images/fg1_10.png\" width=\"400\"/>\n",
    "\n",
    "Then the **marginal**, **conditional** and **joint probabilities** are given by\n",
    "\n",
    "$$\n",
    "p(X=x_i)=\\frac{c_i}{N}\\quad\n",
    "p(Y=y_j)=\\frac{r_j}{N}\\quad\n",
    "p(X=x_i,Y=y_j)=\\frac{n_{ij}}{N}\\quad\n",
    "p(Y=y_j|X=x_i)=\\frac{r_j}{c_i}\n",
    "$$\n",
    "\n",
    "Note that the joint probability $p(X=x_i,Y=y_j)$ is short notation for $p(X=x_i \\cap Y=y_j)$.\n",
    "\n",
    "#### Sum rule:\n",
    "\n",
    "$$\n",
    "p(X) = \\sum_Y p(X,Y) = \\int_Y p(X,Y) dY\n",
    "$$\n",
    "\n",
    "Applying the sum rule as above is called \"marginalizing out $Y$\".\n",
    "\n",
    "#### Product rule:\n",
    "\n",
    "$$\n",
    "p(X,Y) = p(Y|X)p(X)\n",
    "$$\n",
    "\n",
    "Computing $p(Y|X)$ is called \"conditioning on $X$\". The product rule is generalized as follows\n",
    "\n",
    "$$\n",
    "p(X_1,X_2,\\dots,X_K) = p(X_K|X_{K-1},\\dots,X_1)p(X_{K-1},\\dots,X_1),\\dots\n",
    "$$\n",
    "\n",
    "Note that if the *joint distribution* of two random variables factorizes into the product of their marginals, so that $p(X,Y) = p(X)p(Y)$, then $X$ and $Y$ are said to be *statistically independent*. In such case, the product rule becomes $p(Y|X) = p(Y)$.\n",
    "\n",
    "### Bayes Theorem\n",
    "\n",
    "From the *product rule*, we can immediately obtain the [*Bayes' theorem*](https://www.youtube.com/watch?v=HZGCoVF3YvM), using the symmetry property $p(X, Y) = p(Y, X)$ as follows\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& p(X,Y) = p(Y|X)p(X) \\Leftrightarrow \\\\\n",
    "& p(Y|X) = \\frac{p(X, Y)}{p(X)} \\Leftrightarrow \\\\\n",
    "& p(Y|X) = \\frac{p(Y, X)}{p(X)} \\Leftrightarrow \\\\\n",
    "& p(Y|X) = \\frac{p(X|Y)p(Y)}{p(X)}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Using the *sum* and *product rules*, the marginal probability $p(X)$ in the denominator can be expressed in terms of the quantities in the numerator\n",
    "\n",
    "$$\n",
    "p(Y|X) = \\frac{p(X|Y)p(Y)}{\\sum_Y p(X,Y)} = \\frac{p(X|Y)p(Y)}{\\sum_Y p(X|Y)p(Y)}\n",
    "$$\n",
    "\n",
    "An interpretation of the Bayes theorem is that if we had been asked which is the most probable value of $Y$, *before* we observe any value for $X$, then the most complete information we have available is provided by the\n",
    "*prior probability* $p(Y)$. *After* we observe the value of $X$, we can use the Bayes theorem to compute the the *posterior* probability $p(Y|X)$, which represents our updated knowledge after incorporating the evidence provided by the observed data.\n",
    "\n",
    "Let $\\mathbf{w}$ be parameters and $\\mathcal{D}$ be data. Bayes theorem is given by\n",
    "\n",
    "$$\n",
    "p(\\mathbf{w}|\\mathcal{D}) =\n",
    "\\frac{p(\\mathcal{D}|\\mathbf{w})p(\\mathbf{w})}{p(\\mathcal{D})}\n",
    "\\Leftrightarrow\n",
    "\\mathrm{posterior} =\n",
    "\\frac{\\mathrm{likelihood}\\, \\times\\, \\mathrm{prior}}{\\mathrm{evidence}}\n",
    "$$\n",
    "\n",
    "The frequentist paradigm generally quantifies the properties of data driven quantities in the light of the fixed model parameters, while the Bayesian paradigm generally quantifies the properties of unknown model parameters in light of observed data.\n",
    "\n",
    "<img src=\"../images/frequentists_vs_bayesians.png\" width=\"400\"/>\n",
    "\n",
    "\n",
    "## 1.2.1 Probability densities\n",
    "\n",
    "<img src=\"../images/fg1_12.png\" width=\"400\"/>\n",
    "\n",
    "If the probability of a real-valued variable $x$ falling in the interval $(u, u + \\delta)$ is given by $p_x(u)\\delta$, then $p_x(x)$ is called the probability density function over $x$. \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "p(u \\leq x \\leq u + \\delta) =  \\int_{u}^{u + \\delta} p(x)dx = \n",
    "P_x(u + \\delta) - P_x(u) = \n",
    "\\frac{P_x(u + \\delta) - P_x(u)}{\\delta} \\delta\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Then we have that\n",
    "\n",
    "$$\n",
    "\\lim_{\\delta\\to 0} \\frac{P_x(u + \\delta) - P_x(u)}{\\delta} \\delta = \\frac{dP_x(u)}{dx}\\delta = p_x(x)\\delta\n",
    "$$\n",
    "\n",
    "Therefore, the probability that $x$ will lie in an interval $(a, b)$ is then given by\n",
    "\n",
    "$$\n",
    "p(a \\leq x \\leq b) = \\int_a^b p_x(x)dx\n",
    "$$\n",
    "\n",
    "and it must satisfy the following two conditions\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& p_x(x) \\geq 0 \\\\\n",
    "\\int_{-\\infty}^\\infty & p_x(x)dx = 1\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "The probability that $x$ lies in the interval $(−\\infty, z)$ is given by the *cumulative distribution function* (CDF) given by\n",
    "\n",
    "$$\n",
    "P_x(z) = \\int_{-\\infty}^z p_x(x)dx\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\n",
    "p(x) = \\frac{dP_x(x)}{dx}\n",
    "$$\n",
    "\n",
    "If $x$ is a discrete variable, then $p_x(x)$ is sometimes called a *probability mass function* (PMF) because it can be regarded as a set of *probability masses* concentrated at the allowed values of $x$.\n",
    "\n",
    "\n",
    "## 1.2.2 Expectations and covariances\n",
    "\n",
    "The average value of some function $f(x)$ under a probability distribution $p_x(x)$ is called the *expectation* of $f(x)$ and is denoted by $\\mathbb{E}[f]$. The average is weighted by the relative probabilities of the different values of $x$ as follows\n",
    "\n",
    "$$\n",
    "\\mathbb{E}[f] = \\sum_x p_x(x)f(x) = \\int p_x(x)f(x)dx\n",
    "$$\n",
    "\n",
    "For a finite number of $N$ points drawn from the probability distribution, then the expectation can be approximated as a finite sum over these points\n",
    "\n",
    "$$\n",
    "\\mathbb{E}[f] \\approx \\frac{1}{N} \\sum_{n=1}^N f(x_n)\n",
    "$$\n",
    "\n",
    "Note that the expectations of functions of several variables, may use a subscript to indicate which variable is being averaged, i.e., $\\mathbb{E}_x[f(x,y)]$.\n",
    "\n",
    "Whereas the expectation provides a measure of centrality, the variance of a random variable quantifies the spread of that random variable's distribution. Thus, the variance provides a measure of how much variability there is in $f(x)$ around its mean value $\\mathbb{E}[f(x)]$ and is defined as follows\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathrm{var}[f] &= \\mathbb{E}[(f(x) − \\mathbb{E}[f(x)])^2] \\\\\n",
    "&= \\mathbb{E}[f(x)^2 − 2f(x)\\mathbb{E}[f(x)] + \\mathbb{E}[f(x)]^2] \\\\\n",
    "&= \\mathbb{E}[f(x)^2] − \\mathbb{E}[2f(x)\\mathbb{E}[f(x)]] + \\mathbb{E}[\\mathbb{E}[f(x)]^2] \\\\\n",
    "&= \\mathbb{E}[f(x)^2] − 2\\mathbb{E}[f(x)]\\mathbb{E}[f(x)] + \\mathbb{E}[f(x)]^2 \\\\\n",
    "&= \\mathbb{E}[f(x)^2] − \\mathbb{E}[f(x)]^2\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "The covariance expresses the extent to which $x$ and $y$ vary together and is given by\n",
    "\n",
    "$$\n",
    "\\mathrm{cov}[x, y] = \\mathbb{E}_{x,y}[(x − \\mathbb{E}[x])(y − \\mathbb{E}[y])] =\n",
    "\\mathbb{E}_{x,y}[xy] − \\mathbb{E}[x]\\mathbb{E}[y]\n",
    "$$\n",
    "\n",
    "A covariance matrix $\\mathbf{\\Sigma}$ has entries $\\sigma_{ij}$ corresponding to the covariance of variables $i$ and $j$. If two variables are independent, then their covariance vanishes, e.g., $\\mathbf{\\Sigma} = \\mathbf{I}$.\n",
    "\n",
    "\n",
    "## 1.2.4 The Gaussian distribution\n",
    "\n",
    "The *Normal* or *Gaussian* distribution is one of the most important probability distributions for continuous variables. For the case of a single real-valued variable $x$, the distribution is defined as follows\n",
    "\n",
    "$$\n",
    "\\mathcal{N}(x|\\mu,\\sigma^2) =\n",
    "\\frac{1}{(2\\pi\\sigma^2)^{1/2}}\\exp\\Big\\{-\\frac{1}{2\\sigma^2}(x-\\mu)^2\\Big\\}\n",
    "$$\n",
    "\n",
    "and is governed by the parameters $\\mu$, called the *mean*, and $\\sigma^2$, called the *variance*. The square root of the variance $\\sigma$ is called *standard deviation*. An alternative way to represent a Gaussian distribution is by considering a *precision* term $\\beta = \\frac{1}{\\sigma^2}$, denoted by\n",
    "\n",
    "$$\n",
    "\\mathcal{N}(x|\\mu,\\beta^{-1}) =\n",
    "\\frac{\\beta^{1/2}}{\\sqrt{2\\pi\\sigma^2}}\\exp\\Big\\{-\\frac{\\beta}{2}(x - \\mu)^2 \\Big\\}\n",
    "$$"
   ]
  },
  {
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   "execution_count": 8,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 266,
       "width": 400
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_space = np.linspace(-5, 5, 1000)\n",
    "\n",
    "for mean, var, c in [(0, 1, \"g\"), (1, 2, \"r\"), (-1, 3, \"b\")]:\n",
    "    N_distribution = Gaussian(mean, var)\n",
    "    y = [N_distribution.pdf(x) for x in x_space]\n",
    "\n",
    "    plt.plot(x_space, y, color=c, label=\"$\\mathcal{N}$\" + \"$(x|{},{})$\".format(mean, var))\n",
    "\n",
    "plt.xlabel(\"$x$\", fontsize=14)\n",
    "plt.ylabel(\"$\\mathcal{N}(x|\\mu,\\sigma^2)$\", fontsize=14)\n",
    "plt.legend(fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Note that the probability density function is *not an actual probability*, therefore it can take values $\\mathcal{N}(x|\\mu,\\sigma^2) > 1$. We can see that the Gaussian distribution satisfies\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& \\mathcal{N}(x|\\mu,\\sigma^2) > 0 \\\\\n",
    "\\int & \\mathcal{N}(x|\\mu,\\sigma^2)dx = 1\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "The Gaussian distribution can be also defined over a $D$-dimensional vector $\\mathbf{x}$ of continuous variables as follows:\n",
    "\n",
    "$$\n",
    "\\mathcal{N}(\\mathbf{x}|\\mathbf{\\mu},\\mathbf{\\Sigma}) =\n",
    "\\frac{1}{(2\\pi)^{D/2}|\\mathbf{\\Sigma}|^{1/2}}\n",
    "\\exp\\Big\\{-\\frac{1}{2}(\\mathbf{x}-\\mathbf{\\mu})^\\text{T}\\mathbf{\\Sigma}^{-1}(\\mathbf{x}-\\mathbf{\\mu})\\Big\\}\n",
    "$$\n",
    "\n",
    "where the $D$-dimentional vector $\\mathbf{\\mu}$ holds the mean of each dimension, while the $D\\times D$ matrix $\\mathbf{\\Sigma}$ is the covariance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 270,
       "width": 379
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean = np.array([0, 0])\n",
    "sigma = np.array([[1.0, 0.92], [0.92, 2.0]])\n",
    "\n",
    "N_distribution = MultivariateGaussian(mean, sigma)\n",
    "\n",
    "N = 100\n",
    "x1, x2 = np.meshgrid(np.linspace(-5, 5, N), np.linspace(-5, 5, N))\n",
    "p = np.zeros((N, N))\n",
    "for i in range(N):\n",
    "    for j in range(N):\n",
    "        p[i, j] = N_distribution.pdf(np.array([x1[i, j], x2[i, j]]))\n",
    "\n",
    "cp = plt.contourf(x1, x2, p, cmap=\"rainbow\")\n",
    "plt.colorbar(cp)\n",
    "plt.xlabel(\"$x_1$\", fontsize=14)\n",
    "plt.ylabel(\"$x_2$\", fontsize=14)\n",
    "plt.axis([-3, 3, -3, 3])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maximum likelihood\n",
    "\n",
    "Consider we have a data set of observations $\\mathsf{x}=(x_1,\\dots,x_N)^\\text{T}$ drawn independently from a Gaussian distribution. Data points that are drawn independently from the same distribution are said to be *independent and identically distributed*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 378
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_distribution = Gaussian(0, 1)\n",
    "x_sample_data = N_distribution.draw(5)\n",
    "y_sample_data = [N_distribution.pdf(x) for x in x_sample_data]\n",
    "\n",
    "x_space = np.linspace(-5, 5, 100)\n",
    "y = [N_distribution.pdf(x) for x in x_space]\n",
    "\n",
    "plt.scatter(x_sample_data, y_sample_data, label=\"Training data\")\n",
    "plt.plot(x_space, y, color=\"g\", label=\"$\\mathcal{N}(x|0,1)$\")\n",
    "plt.legend(fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because the data are independent, the likelihood function of the univariate Gaussian is as follows,\n",
    "\n",
    "$$\n",
    "p(\\mathsf{x}|\\mu,\\sigma^2) = \\prod_{n=1}^N \\mathcal{N}(x_n|\\mu, \\sigma^2)\n",
    "$$\n",
    "\n",
    "which corresponds to the product of the blue points in the figure above. Therefore, in order to find the unknown parameters $\\mu$ and $\\sigma^2$ is to use the observed data set and find the parameter values that maximize the likelihood function.\n",
    "\n",
    "The log likelihood function can be written as follows\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\ln p(\\mathsf{x}|\\mu,\\sigma^2) &= \\ln \\Bigg[ \\prod_{n=1}^N \\mathcal{N}(x_n|\\mu, \\sigma^2) \\Bigg] \\\\\n",
    "&= \\sum_{n=1}^N \\ln\\mathcal{N}(x_n|\\mu, \\sigma^2) \\\\\n",
    "&\\overset{(1.46)}= \\sum_{n=1}^N \\ln \\bigg(\n",
    "\\frac{1}{(2\\pi\\sigma^2)^{1/2}}\\exp\\Big\\{-\\frac{1}{2\\sigma^2}(x_n-\\mu)^2\\Big\\} \\bigg) \\\\\n",
    "&= \\sum_{n=1}^N \\ln \\bigg( \\frac{1}{(2\\pi\\sigma^2)^{1/2}} \\bigg) +\n",
    "\\sum_{n=1}^N \\ln \\bigg(\\exp\\Big\\{-\\frac{1}{2\\sigma^2}(x_n-\\mu)^2\\Big\\} \\bigg) \\\\\n",
    "&= N\\ln \\bigg( \\frac{1}{(2\\pi\\sigma^2)^{1/2}} \\bigg) -\n",
    "\\sum_{n=1}^N \\frac{1}{2\\sigma^2}(x_n-\\mu)^2 \\\\\n",
    "&= N\\ln1 - N\\ln (2\\pi\\sigma^2)^{1/2} - \\frac{1}{2\\sigma^2} \\sum_{n=1}^N (x_n-\\mu)^2 \\\\\n",
    "&\\overset{\\ln1=0}= -N\\ln (2\\pi\\sigma^2)^{1/2} - \\frac{1}{2\\sigma^2} \\sum_{n=1}^N (x_n-\\mu)^2 \\\\\n",
    "&\\overset{\\ln x^y=y\\ln x}= -\\frac{N}{2}\\ln 2\\pi\\sigma^2 - \\frac{1}{2\\sigma^2} \\sum_{n=1}^N (x_n-\\mu)^2 \\\\\n",
    "&= -\\frac{N}{2}\\ln 2\\pi -\\frac{N}{2}\\ln\\sigma^2 - \\frac{1}{2\\sigma^2} \\sum_{n=1}^N (x_n-\\mu)^2\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "In the machine learning literature, the negative log of the likelihood function is called an error function. Since the negative logarithm is a monotonically decreasing function, maximizing the likelihood is equivalent to minimizing the error. The following figure depicts the likelihood of $\\mu$ against $\\sigma^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 270,
       "width": 394
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu_space = np.linspace(-1, 1, 100)\n",
    "var_space = np.linspace(0, 2, 100)\n",
    "mu_mesh, var_mesh = np.meshgrid(mu_space, var_space)\n",
    "ll = np.zeros((mu_space.size, var_space.size))\n",
    "\n",
    "for i, mu in enumerate(mu_space):\n",
    "    for j, var in enumerate(var_space):\n",
    "        ll[i, j] = Gaussian(mu, var).likelihood_iid(x_sample_data)\n",
    "\n",
    "cp = plt.contourf(mu_mesh, var_mesh, ll.T, cmap=\"rainbow\")\n",
    "plt.colorbar(cp)\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(0, 2)\n",
    "plt.xlabel(\"$\\mu$\", fontsize=14)\n",
    "plt.ylabel(\"$\\sigma^2$\", fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then by maximizing with respect to $\\mu$, we obtain the following solution\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& \\frac{\\partial \\ln p(\\mathsf{x}|\\mu,\\sigma^2)}{\\partial \\mu} = 0 \\Leftrightarrow \\\\\n",
    "& \\frac{\\partial}{\\partial \\mu}\n",
    "\\bigg( \\frac{N}{2}\\ln 2\\pi -\\frac{N}{2}\\ln\\sigma^2 - \\frac{1}{2\\sigma^2} \\sum_{n=1}^N (x_n-\\mu)^2 \\bigg) = 0\n",
    "\\Leftrightarrow \\\\\n",
    "& \\frac{\\partial}{\\partial \\mu} \\bigg( \\frac{1}{2\\sigma^2} \\sum_{n=1}^N (x_n-\\mu)^2 \\bigg) = 0 \\Leftrightarrow \\\\\n",
    "& \\frac{\\partial}{\\partial \\mu} \\sum_{n=1}^N (x_n-\\mu)^2 = 0 \\Leftrightarrow \\\\\n",
    "& \\sum_{n=1}^N (2\\mu - 2x_n) = 0 \\Leftrightarrow 2\\sum_{n=1}^N (\\mu - x_n) = 0 \\Leftrightarrow \\\\\n",
    "& N\\mu - \\sum_{n=1}^N x_n = 0 \\Leftrightarrow N\\mu = \\sum_{n=1}^N x_n \\Leftrightarrow \\\\\n",
    "& \\mu_{ML} = \\frac{1}{N}\\sum_{n=1}^N x_n\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "which is the *sample mean* of the observed values $\\mathsf{x}$. In a similar manner, maximizing with respect to $\\sigma^2$, we obtain the maximum likelihood solution for the variance as follows\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& \\frac{\\partial \\ln p(\\mathsf{x}|\\mu,\\sigma^2)}{\\partial \\sigma^2} = 0 \\Leftrightarrow \\\\\n",
    "& \\frac{\\partial}{\\partial \\sigma^2}\n",
    "\\bigg( \\frac{N}{2}\\ln 2\\pi -\\frac{N}{2}\\ln\\sigma^2 - \\frac{1}{2\\sigma^2} \\sum_{n=1}^N (x_n-\\mu)^2 \\bigg) = 0\n",
    "\\Leftrightarrow \\\\\n",
    "& \\frac{\\partial}{\\partial \\sigma^2}\n",
    "\\bigg( -\\frac{1}{2\\sigma^2} \\sum_{n=1}^N (x_n-\\mu)^2 - \\frac{N}{2}\\ln\\sigma^2 \\bigg) = 0\n",
    "\\Leftrightarrow \\\\\n",
    "& \\frac{\\partial}{\\partial \\sigma^2} \\bigg(-\\frac{1}{2\\sigma^2} \\sum_{n=1}^N (x_n-\\mu)^2 \\bigg) +\n",
    "\\frac{\\partial}{\\partial \\sigma^2} \\bigg(-\\frac{N}{2}\\ln\\sigma^2 \\bigg) = 0\n",
    "\\Leftrightarrow \\\\\n",
    "& \\frac{\\partial}{\\partial \\sigma^2} \\bigg(-(2\\sigma^2)^{-1} \\sum_{n=1}^N (x_n-\\mu)^2 \\bigg) +\n",
    "- \\frac{N}{2\\sigma^2} = 0\n",
    "\\Leftrightarrow \\\\\n",
    "& \\frac{1}{4\\sigma^4} \\sum_{n=1}^N (x_n-\\mu)^2 - \\frac{N}{2\\sigma^2} = 0\n",
    "\\Leftrightarrow \\\\\n",
    "& \\frac{1}{4\\sigma^4} \\sum_{n=1}^N (x_n-\\mu)^2 = \\frac{N}{2\\sigma^2}\n",
    "\\Leftrightarrow \\\\\n",
    "& \\sigma_{ML}^2 = \\frac{1}{N} \\sum_{n=1}^N (x_n-\\mu_{ML})^2\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "which is the *sample variance* measured with respect to the sample mean $\\mu_{ML}$.\n",
    "\n",
    "A problem that arises in the context of our solutions for the maximum likelihood approach is that it systematically underestimates the variance of the Gaussian distribution. This is an example of a phenomenon called bias and is related to the problem of over-fitting encountered in the context of polynomial curve fitting. First note that the maximum likelihood solutions $\\mu_{ML}$ and $\\sigma_{ML}$ are functions of the data set values $x_n$. Now, consider the expectations of these quantities with respect to the data set values, which themselves come from a Gaussian distribution with parameters $\\mu$ and $\\sigma^2$, given by\n",
    "\n",
    "$$\n",
    "\\mathbb{E}[\\mu_{ML}] = \\mathbb{E}\\bigg[ \\frac{1}{N} \\sum_{n=1}^N x_n \\bigg] = \n",
    "\\frac{1}{N} \\sum_{n=1}^N \\mathbb{E}[x_n] = \\frac{1}{N} N \\mu = \\mu\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbb{E}[\\sigma_{ML}^2] &= \\mathbb{E}\\bigg[ \\frac{1}{N} \\sum_{n=1}^N (x_n-\\mu_{ML})^2 \\bigg] \\\\\n",
    "&= \\frac{1}{N} \\mathbb{E}\\bigg[ \\sum_{n=1}^N (x_n-\\mu_{ML})^2 \\bigg] \\\\\n",
    "&= \\frac{1}{N} \\mathbb{E}\\bigg[ \\sum_{n=1}^N (x_n^2-2x_n\\mu_{ML}+\\mu_{ML}^2) \\bigg] \\\\\n",
    "&= \\frac{1}{N} \\Bigg(\n",
    "\\mathbb{E}\\bigg[ \\sum_{n=1}^N x_n^2 \\bigg] - \n",
    "\\mathbb{E}\\bigg[ \\sum_{n=1}^N 2x_n\\mu_{ML} \\bigg] +\n",
    "\\mathbb{E}\\bigg[ \\sum_{n=1}^N \\mu_{ML}^2 \\bigg]\n",
    "\\Bigg) \\\\\n",
    "&\\overset{(1.50)}= \\mu^2 + \\sigma^2 - \n",
    "\\frac{1}{N} \\Bigg(\n",
    "\\mathbb{E}\\bigg[ \\sum_{n=1}^N 2x_n\\mu_{ML} \\bigg] +\n",
    "\\mathbb{E}\\bigg[ \\sum_{n=1}^N \\mu_{ML}^2 \\bigg]\n",
    "\\Bigg) \\\\\n",
    "&\\overset{(1.55)}= \\mu^2 + \\sigma^2 - \n",
    "\\frac{2}{N} \\mathbb{E}\\bigg[ \\sum_{n=1}^N x_n\\bigg( \\frac{1}{N}\\sum_{n=1}^N x_n \\bigg) \\bigg] +\n",
    "\\mathbb{E}\\bigg[ \\bigg( \\frac{1}{N}\\sum_{n=1}^N x_n \\bigg)^2 \\bigg] \\\\\n",
    "&= \\mu^2 + \\sigma^2 - \n",
    "\\frac{2}{N^2} \\mathbb{E}\\bigg[ \\sum_{n=1}^N x_n\\bigg( \\sum_{n=1}^N x_n \\bigg) \\bigg] +\n",
    "\\frac{1}{N^2} \\mathbb{E}\\bigg[ \\bigg( \\sum_{n=1}^N x_n \\bigg)^2 \\bigg] \\\\\n",
    "&= \\mu^2 + \\sigma^2 - \n",
    "\\frac{2}{N^2} \\mathbb{E}\\bigg[ \\bigg( \\sum_{n=1}^N x_n \\bigg)^2 \\bigg] +\n",
    "\\frac{1}{N^2} \\mathbb{E}\\bigg[ \\bigg( \\sum_{n=1}^N x_n \\bigg)^2 \\bigg] \\\\\n",
    "&= \\mu^2 + \\sigma^2 - \n",
    "\\frac{1}{N^2} \\mathbb{E}\\bigg[ \\bigg( \\sum_{n=1}^N x_n \\bigg)^2 \\bigg] \\\\\n",
    "&= \\mu^2 + \\sigma^2 - \\frac{1}{N^2}(N^2\\mu^2 + N\\sigma^2)) \\\\\n",
    "&= \\mu^2 + \\sigma^2 - \\mu^2 + \\frac{1}{N}\\sigma^2 \\\\\n",
    "&= \\frac{N-1}{N}\\sigma^2 \\\\\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Therefore, on average the maximum likelihood estimate obtains the correct mean but it underestimates the true variance by a factor $(N − 1)/N$. The estimate for the unbiased variance parameter is given by\n",
    "\n",
    "$$\n",
    "\\tilde{\\sigma}^2 = \\frac{N}{N-1}\\sigma_{ML}^2 = \\frac{1}{N-1} \\sum_{n=1}^N (x_n-\\mu_{ML})^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 266,
       "width": 647
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N_distribution.ml(x_sample_data, unbiased=False)\n",
    "y_biased = [N_distribution.pdf(x) for x in x_space]\n",
    "N_distribution.ml(x_sample_data, unbiased=True)\n",
    "y_unbiased = [N_distribution.pdf(x) for x in x_space]\n",
    "\n",
    "plt.plot(x_space, y, color=\"g\", label=\"True Gaussian distribution\")\n",
    "plt.plot(x_space, y_biased, color=\"r\", ls=\":\", label=\"Biased maximum likelihood\")\n",
    "plt.plot(x_space, y_unbiased, color=\"b\", ls=\":\", label=\"Unbiased maximum likelihood\")\n",
    "plt.xlabel(\"$x$\", fontsize=14)\n",
    "plt.legend(bbox_to_anchor=(1, 0.7), loc=2, borderaxespad=1, fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2.5 Curve fitting re-visited\n",
    "\n",
    "Now, lets return to the curve fitting example and examine it from a probabilistic perspective, thereby gaining some insights into error functions and regularization, as well as, taking us towards a full Bayesian treatment. We shall assume that, the target variable $t$ has a Gaussian distribution having mean equal to $y(x,\\mathbf{w})$ of the polynomial curve, given by\n",
    "\n",
    "$$\n",
    "p(t|x,\\mathbf{w},\\beta) = \\mathcal{N}(t|y(x,\\mathbf{w}),\\beta^{-1})\n",
    "$$\n",
    "\n",
    "where we have defined $\\beta$ to be the precision parameter, corresponding to the inverse variance.\n",
    "\n",
    "<img src=\"../images/fg1_16.png\" width=\"400\"/>\n",
    "\n",
    "Each input point $x$ defines a Gaussian distribution located into prediction of $y(x,\\mathbf{w})$. We plot the Gaussian distribution heatmap of the values of $x$ against $t$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 270,
       "width": 388
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_sample, t_sample = generate_toy_data(sin, 50, 0.3)\n",
    "\n",
    "feature = PolynomialFeature(4)\n",
    "x_features = feature.transform(x_sample)\n",
    "model = LinearRegression()\n",
    "model.fit(x_features, t_sample)\n",
    "\n",
    "x_space = np.arange(0, 1, 0.01)\n",
    "t_space = np.arange(-2, 2, 0.01)\n",
    "X, Y = np.meshgrid(x_space, t_space)\n",
    "Z = np.zeros((x_space.size, t_space.size))\n",
    "for i, x in enumerate(x_space):\n",
    "    # create the Gaussian distribution for a given input value\n",
    "    predicted_mu, _ = model.predict(feature.transform(x))\n",
    "    g = Gaussian(predicted_mu[0], 0.3)\n",
    "    for j, t in enumerate(t_space):\n",
    "        # compute the value of the Gaussian for each target value\n",
    "        Z[i, j] = g.pdf(t)\n",
    "\n",
    "cp = plt.contourf(X, Y, Z.T.reshape(X.shape), cmap=\"rainbow\", levels=40)\n",
    "plt.scatter(x_sample, t_sample, color=\"snow\")\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(-2, 2)\n",
    "plt.xlabel(\"$x$\", fontsize=14)\n",
    "plt.ylabel(\"$t$\", fontsize=14)\n",
    "plt.colorbar(cp)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Then, we can use the training data $\\mathsf{x,t}$ to determine the values of the unknown parameters $\\mathbf{w},\\beta$ by maximum likelihood. Assuming the data are i.i.d, the likelihood function is given by\n",
    "\n",
    "$$\n",
    "p(\\mathsf{t}|\\mathsf{x},\\mathbf{w},\\beta) = \\prod_{n=1}^N \\mathcal{N}(t_n|y(x,\\mathbf{w}),\\beta^{-1})\n",
    "$$\n",
    "\n",
    "Similar to the Gaussian distribution earlier, we maximize the logarithm of the likelihood function in the form\n",
    "\n",
    "$$\n",
    "\\ln p(\\mathsf{t}|\\mathsf{x},\\mathbf{w},\\beta) =\n",
    "-\\frac{\\beta}{2}\\sum_{n=1}^N (y(x,\\mathbf{w}) - t_n)^2 + \\frac{N}{2}\\ln\\beta - \\frac{N}{2}\\ln2\\pi\n",
    "$$\n",
    "\n",
    "For determining the maximum likelihood solution for the polynomial coefficients $\\mathbf{w}_{ML}$, we can omit the terms that do not depend on $\\mathbf{w}$. Since the $\\beta$ does not alter the location of the function it can be replaced by $1$. Therefore, the maximization is equivalent to minimizing the *sum of squares error function*, as presented the [polynomial curve fitting example](#Error-Function). The sum of squares error function has arisen as a consequence of maximizing the likelihood under the assumption of a Gaussian noise distribution!\n",
    "\n",
    "As a final step, we can also use maximum likelihood to determine the precision parameter $\\beta$, as follows:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "& \\frac{\\partial}{\\partial\\beta} \\ln p(\\mathsf{t}|\\mathsf{x},\\mathbf{w},\\beta) = 0 \\Leftrightarrow \\\\\n",
    "& \\frac{\\partial}{\\partial\\beta}\n",
    "\\Big [\n",
    "-\\frac{\\beta}{2}\\sum_{n=1}^N (y(x,\\mathbf{w}) - t_n)^2 + \\frac{N}{2}\\ln\\beta - \\frac{N}{2}\\ln2\\pi\n",
    "\\Big ] = 0\n",
    "\\Leftrightarrow \\\\\n",
    "& \\frac{\\partial}{\\partial\\beta}\n",
    "\\Big [\n",
    "-\\frac{\\beta}{2}\\sum_{n=1}^N (y(x,\\mathbf{w}) - t_n)^2\n",
    "\\Big ] +\n",
    "\\frac{\\partial}{\\partial\\beta}\n",
    "\\Big [\n",
    "\\frac{N}{2}\\ln\\beta\n",
    "\\Big ] = 0\n",
    "\\Leftrightarrow \\\\\n",
    "& -\\frac{1}{2}\\sum_{n=1}^N (y(x,\\mathbf{w}) - t_n)^2 + \\frac{N}{2}\\frac{1}{\\beta} = 0\n",
    "\\Leftrightarrow \\\\\n",
    "& \\sum_{n=1}^N (y(x,\\mathbf{w}) - t_n)^2 = \\frac{N}{\\beta}\n",
    "\\Leftrightarrow \\\\\n",
    "& \\frac{1}{\\beta_{ML}} = \\frac{1}{N}\\sum_{n=1}^N (y(x,\\mathbf{w}) - t_n)^2\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Since we have a probabilistc model, we can use the predictive distribution that gives the probability distribution over $t$, rather than a simple point estimate.\n",
    "\n",
    "$$\n",
    "p(t|x,\\mathbf{w}_{ML},\\beta_{ML}) = \\mathcal{N}(t|y(x,\\mathbf{w}_{ML}),\\beta_{ML}^{-1})\n",
    "$$\n",
    "\n",
    "We can further introduce a prior distribution over the polynomial coefficients $\\mathbf{w}$, in order to take a step towards a more Bayesian approach. Consider for instance a Gaussian prior of the form\n",
    "\n",
    "$$\n",
    "p(\\mathbf{w}|\\alpha) = \\mathcal{N}(\\mathbf{w}|\\mathbf{0},\\alpha^{-1}\\mathbf{I}) = \\Big(\\frac{\\alpha}{2\\pi}^{(M+1)/2}\\Big)\\exp\\Big\\{-\\frac{\\alpha}{2}\\mathbf{w}^{\\text{T}}\\mathbf{w}\\Big\\}\n",
    "$$\n",
    "\n",
    "where $\\alpha$ is the precision of the multivariate Gaussian, and $M$ is the order of the polynomial, that is, the dimension of the paremeter vector $\\mathbf{w}$. Then from the Bayes theorem we have that\n",
    "\n",
    "$$\n",
    "p(\\mathbf{w}|\\mathsf{x},\\mathsf{t},\\alpha,\\beta) \\propto p(\\mathsf{t}|\\mathsf{x},\\mathbf{w},\\beta) p(\\mathbf{w}|\\alpha)\n",
    "$$\n",
    "\n",
    "Therefore, we can determine $\\mathbf{w}$, by maximizing the posterior distribution. This technique is known as *maximum posterior* or MAP inference. The maximum of the posterior is given by the minimum of the negative logarithm, which it can be proved to be\n",
    "\n",
    "$$\n",
    "\\frac{\\beta}{2}\\sum_{n=1}^N (y(x,\\mathbf{w}) - t_n)^2 + \\frac{\\alpha}{2}\\mathbf{w}^{\\text{T}}\\mathbf{w}\n",
    "$$\n",
    "\n",
    "Thus we see that maximizing the posterior distribution is equivalent to minimizing the regularized sum of squared error function encountered in [Regularization](#Regularization), where $\\lambda=\\alpha/\\beta$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1.6 Information Theory\n",
    "\n",
    "*How much information is received when we observe a specific variable?*\n",
    "\n",
    "Consider for instance the event of seeing an alien spaceship appearing in the sky. We have never seen one and we would be extremely surprised if one day such an event occured, since it is unexpected given our current knowledge. Therefore, the amount of information can be viewed as the *degree of surprise* on learning the value of $x$. The measure of information content is therefore depend on the probability distribution $p(x)$ and in particular is given by the logarithm of $p(x)$ as follows,\n",
    "\n",
    "$$\n",
    "\\text{h}(x)=-\\log_2p(x)\n",
    "$$\n",
    "\n",
    "where the negative sign ensures that $h(x) \\geq 0$. When the base of the logarithm is $2$ the units of $h(x)$ are **bits**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 266,
       "width": 380
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def h(prob: float) -> float:\n",
    "    if not 0 <= prob <= 1:\n",
    "        raise ValueError(\"Probability should be [0,1].\")\n",
    "    elif prob == 0:\n",
    "        return float(\"-inf\")\n",
    "    else:\n",
    "        return -math.log2(prob)\n",
    "\n",
    "\n",
    "px_space = np.linspace(0, 1, 100)\n",
    "y = [h(px) for px in px_space]\n",
    "\n",
    "plt.plot(px_space, y)\n",
    "plt.xlabel(\"Probability of event x\", fontsize=14)\n",
    "plt.ylabel(\"Information content (bits)\", fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The average amount of information is obtained by taking the expectation over the information content, given by,\n",
    "\n",
    "$$\n",
    "\\text{H}[x] = -\\sum_{x} p(x)h(x) = -\\sum_{x} p(x)\\log_2 p(x)\n",
    "$$\n",
    "\n",
    "This important quantity is called *entropy* of the random variable $X$. Consider a discrete random variable $X$ having two possible values $x_1$ and $x_2$ with probabilities $p$ and $1-p$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 268,
       "width": 390
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def entropy(probs):\n",
    "    if 0 in probs:\n",
    "        return 0\n",
    "    else:\n",
    "        return sum([px * h(px) for px in probs])\n",
    "\n",
    "\n",
    "px_space = np.linspace(0, 1, 100)\n",
    "y = [entropy([px, 1 - px]) for px in px_space]\n",
    "\n",
    "plt.plot(px_space, y)\n",
    "plt.xlabel(\"Probability of event $x_1$\", fontsize=14)\n",
    "plt.ylabel(\"Entropy (bits)\", fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the entropy is maximized when the two events are equiprobable, that is, for uniform distributions. The entory is also defined in a similar way for continous random variables and is called *differential entropy*:\n",
    "\n",
    "$$\n",
    "\\text{H}[\\mathbf{x}] = -\\int p(\\mathbf{x}) \\ln p(\\mathbf{x})\\text{d}\\mathbf{x}\n",
    "$$\n",
    "\n",
    "In the case of a joint distribution $p(\\mathbf{x},\\mathbf{y})$, the average additional information needed to specify $\\mathbf{y}$ given that the value of $\\mathbf{x}$ is already known, is called *conditional entropy*, and is given by\n",
    "\n",
    "$$\n",
    "\\text{H}[\\mathbf{y}|\\mathbf{x}] = \n",
    "-\\int p(\\mathbf{x},\\mathbf{y}) \\ln p(\\mathbf{y}|\\mathbf{x})\\text{d}\\mathbf{x}\\text{d}\\mathbf{y}\n",
    "$$\n",
    "\n",
    "Moreover it is easily seen, using the product rule, that the conditional entropy satisfies the relation,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\text{H}[\\mathbf{x},\\mathbf{y}] &= \n",
    "-\\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln p(\\mathbf{x},\\mathbf{y})\\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \\\\\n",
    "&= -\\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln \\big(p(\\mathbf{y}|\\mathbf{x})p(\\mathbf{x})\\big)\\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \\\\\n",
    "&= -\\int\\int p(\\mathbf{x},\\mathbf{y}) \\big(\\ln p(\\mathbf{y}|\\mathbf{x}) + \\ln p(\\mathbf{x})\\big) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \\\\\n",
    "&= -\\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln p(\\mathbf{y}|\\mathbf{x}) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y}\n",
    "-\\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln p(\\mathbf{x}) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \\\\\n",
    "&= -\\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln p(\\mathbf{y}|\\mathbf{x}) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y}\n",
    "-\\int\\int p(\\mathbf{x},\\mathbf{y})\\text{d}\\mathbf{y} \\ln p(\\mathbf{x}) \\text{d}\\mathbf{x} \\\\\n",
    "&= -\\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln p(\\mathbf{y}|\\mathbf{x}) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y}\n",
    "-\\int p(\\mathbf{x}) \\ln p(\\mathbf{x}) \\text{d}\\mathbf{x} \\\\\n",
    "&= \\text{H}[\\mathbf{y}|\\mathbf{x}] + \\text{H}[\\mathbf{x}]\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "stating that the information needed to describe $\\mathbf{x}$ and $\\mathbf{y}$ is given by the information needed to describe $\\mathbf{x}$ alone plus the additional information to specify $\\mathbf{y}$.\n",
    "\n",
    "## 1.6.1 Relative entropy and mutual information\n",
    "\n",
    "Consider some unknown distribution $p(\\mathbf{x})$ that we have modelled using an approximate distribution $q(\\mathbf{x})$. Then, the average *additional* information required to specify a value of $\\mathbf{x}$ as a result of using $q(\\mathbf{x})$ instead of $p(\\mathbf{x})$ is given by\n",
    "\n",
    "$$\n",
    "\\text{KL}(p||q) = \n",
    "-\\int p(\\mathbf{x})\\ln q(\\mathbf{x})d\\mathbf{x} \n",
    "-\\bigg( -\\int p(\\mathbf{x}) \\ln q(\\mathbf{x})d\\mathbf{x} \\bigg) =\n",
    "-\\int p(\\mathbf{x}) \\big( \\ln q(\\mathbf{x}) - \\ln p(\\mathbf{x}) \\big) d\\mathbf{x} = \n",
    "-\\int p(\\mathbf{x}) \\ln\\big( \\frac{q(\\mathbf{x})}{p(\\mathbf{x})} \\big) d\\mathbf{x}.\n",
    "$$\n",
    "\n",
    "This is known as the *relative entropy* or *Kullback-Leibler divergence* between distributions $p(\\mathbf{x})$ and $q(\\mathbf{x})$. Note that it is not a symmetrical quantity, that is to say $\\text{KL}(p||q) \\neq \\text{KL}(q||p)$. Moreover the Kullback-Leibler divergence satisfies $\\text{KL}(p||q) \\geq 0$, where the equality holds if, and only if, $p(\\mathbf{x}) = q(\\mathbf{x})$. Thus, we can interpret the Kullback-Leibler divergence as a measure of dissimilarity of the two distributions.\n",
    "\n",
    "Since the most efficient compression is achieved when we know the true distribution, otherwise additional information is required, there is an important relationship between data compression and density estimation.\n",
    "\n",
    "Suppose we are trying to approximate the unknown distribution using some parametric distribution $q(\\mathbf{x}|\\mathbf{\\theta})$, governed by a set of adjustable parameters $\\mathbf{\\theta}$, for instance a multivariate Gaussian distribution. One way to determine $\\mathbf{\\theta}$ is to minimize the Kullback-Leibler divergence between $p(\\mathbf{x})$ and $q(\\mathbf{x}|\\mathbf{\\theta})$. This is impossible since we do not know $p(\\mathbf{x})$. However, if we have observed a finite set of training points $\\mathbf{x}_n$ drawn from $p(\\mathbf{x})$, then the expectation with respect to $p(\\mathbf{x})$ can be approximated by a finite sum over these points, using $(1.35)$, so that,\n",
    "\n",
    "$$\n",
    "\\text{KL}(p||q) \\approx \n",
    "\\frac{1}{N} \\sum_{n=1}^{N} \\big( -\\ln q(\\mathbf{x}_n|\\mathbf{\\theta}) + \\ln p(\\mathbf{x}_n) \\big)\n",
    "$$\n",
    "\n",
    "Since the second term is independent of $\\mathbf{\\theta}$, minimizing this **approximated** Kullback-Leibler divergence is equivalent to minimizing the log likelihood function of $q(\\mathbf{x}_n|\\mathbf{\\theta})$ evaluated on the training set.\n",
    "\n",
    "### Mutual information\n",
    "\n",
    "Consider the joint distribution $p(\\mathbf{x},\\mathbf{y})$ between two sets of variables $\\mathbf{x}$ and $\\mathbf{y}$. If the sets are independent, then $p(\\mathbf{x},\\mathbf{y})=p(\\mathbf{x})(\\mathbf{y})$. If the variables are not independent, we can measure whether they are *close* to being independent* by considering the Kullback-Leibler divergence between the joint distribution and the product of their marginals, given by\n",
    "\n",
    "$$\n",
    "\\text{I}[\\mathbf{x},\\mathbf{y}] = \\text{KL}(p(\\mathbf{x},\\mathbf{y})||p(\\mathbf{x})p(\\mathbf{y})) =\n",
    "-\\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln \\bigg( \\frac{p(\\mathbf{x})p(\\mathbf{y})}{p(\\mathbf{x},\\mathbf{y})} \\bigg) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \n",
    "$$\n",
    "\n",
    "which is called the *mutual information* of variables $\\mathbf{x}$ and $\\mathbf{y}$. The mutual information satisfies $\\text{I}[\\mathbf{x},\\mathbf{y}] \\geq 0$ where the equality holds if, and only if, $\\mathbf{x}$ and $\\mathbf{y}$ are independent. Moreover, using the sum and product rules of probability, we can prove that the mutual information is related to the conditional entropy,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\text{I}[\\mathbf{x},\\mathbf{y}] &= \n",
    "-\\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln \\bigg( \\frac{p(\\mathbf{x})p(\\mathbf{y})}{p(\\mathbf{x},\\mathbf{y})} \\bigg) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \\\\\n",
    "&= -\\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln \\bigg( \\frac{p(\\mathbf{x})p(\\mathbf{y})}{p(\\mathbf{x}|\\mathbf{y})p(\\mathbf{y})} \\bigg) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \\\\\n",
    "&= -\\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln \\bigg( \\frac{p(\\mathbf{x})}{p(\\mathbf{x}|\\mathbf{y})} \\bigg) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \\\\\n",
    "&= -\\int\\int p(\\mathbf{x},\\mathbf{y}) \\bigg( \\ln p(\\mathbf{x}) - \\ln p(\\mathbf{x}|\\mathbf{y}) \\bigg) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \\\\\n",
    "&= -\\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln p(\\mathbf{x}) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \n",
    "+ \\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln p(\\mathbf{x}|\\mathbf{y}) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \\\\\n",
    "&= -\\int\\int p(\\mathbf{x},\\mathbf{y})\\text{d}\\mathbf{y} \\ln p(\\mathbf{x}) \\text{d}\\mathbf{x}\n",
    "+ \\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln p(\\mathbf{x}|\\mathbf{y}) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \\\\\n",
    "&= -\\int p(\\mathbf{x}) \\ln p(\\mathbf{x}) \\text{d}\\mathbf{x}\n",
    "+ \\int\\int p(\\mathbf{x},\\mathbf{y}) \\ln p(\\mathbf{x}|\\mathbf{y}) \\text{d}\\mathbf{x}\\text{d}\\mathbf{y} \\\\\n",
    "&= \\text{H}[\\mathbf{x}] - \\text{H}[\\mathbf{x}|\\mathbf{y}] = \\text{H}[\\mathbf{y}] - \\text{H}[\\mathbf{y}|\\mathbf{x}]\n",
    "\\end{aligned}\n",
    "$$"
   ]
  }
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